Problem: Solve for $x$ and $y$ using substitution. ${x-5y = -3}$ ${y = 2x-12}$
Explanation: Since $y$ has already been solved for, substitute $2x-12$ for $y$ in the first equation. ${x - 5}{(2x-12)}{= -3}$ Simplify and solve for $x$ $x-10x + 60 = -3$ $-9x+60 = -3$ $-9x+60{-60} = -3{-60}$ $-9x = -63$ $\dfrac{-9x}{{-9}} = \dfrac{-63}{{-9}}$ ${x = 7}$ Now that you know ${x = 7}$ , plug it back into $\thinspace {y = 2x-12}\thinspace$ to find $y$ ${y = 2}{(7)}{ - 12}$ $y = 14 - 12$ $y = 2$ You can also plug ${x = 7}$ into $\thinspace {x-5y = -3}\thinspace$ and get the same answer for $y$ : ${(7)}{ - 5y = -3}$ ${y = 2}$